Organization and clasification of trajectories in the time-delayed Mackey-Glass system

TL;DR

This paper presents an electronic implementation of the Mackey-Glass system to analyze and classify coexisting trajectories in phase space, using a novel symbolic algorithm and exploring parameter variations.

Contribution

It introduces a new electronic setup for the Mackey-Glass system and a symbolic classification method for coexisting solutions in phase space.

Findings

Multiple coexisting periodic and aperiodic solutions identified

Symbolic algorithm effectively classifies solution types

Phase space explored across various initial conditions

Abstract

Using a novel electronic implementation of a well-known time-delayed system, the Mackey-Glass (MG) system, we investigate the organization of the trajectories in the phase space, and classify the coexisting solutions, both, in observations and in model simulations. The numerical simultations are performed using a discrete-time equation that approximates the exact solutions of the MG model and in particular, models the delay line in the electronic circuit. In wide parameter regions, different periodic or aperiodic solutions, but with similar waveforms exhibiting the alternation of peaks of different amplitudes, coexist. A symbolic algorithm is proposed to classify those solutions. The system's phase-space was explored by varying the parameter values of two families of initial functions.